# pam

0th

Percentile

##### Partitioning Around Medoids

Partitioning (clustering) of the data into k clusters “around medoids”, a more robust version of K-means.

Keywords
cluster
##### Usage
pam(x, k, diss = inherits(x, "dist"),
metric = c("euclidean", "manhattan"),
medoids = NULL, stand = FALSE, cluster.only = FALSE,
do.swap = TRUE,
keep.diss = !diss && !cluster.only && n < 100,
keep.data = !diss && !cluster.only,
pamonce = FALSE, trace.lev = 0)
##### Arguments
x

data matrix or data frame, or dissimilarity matrix or object, depending on the value of the diss argument.

In case of a matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values (NAs) are allowed---as long as every pair of observations has at least one case not missing.

In case of a dissimilarity matrix, x is typically the output of daisy or dist. Also a vector of length n*(n-1)/2 is allowed (where n is the number of observations), and will be interpreted in the same way as the output of the above-mentioned functions. Missing values (NAs) are not allowed.

k

positive integer specifying the number of clusters, less than the number of observations.

diss

logical flag: if TRUE (default for dist or dissimilarity objects), then x will be considered as a dissimilarity matrix. If FALSE, then x will be considered as a matrix of observations by variables.

metric

character string specifying the metric to be used for calculating dissimilarities between observations. The currently available options are "euclidean" and "manhattan". Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences. If x is already a dissimilarity matrix, then this argument will be ignored.

medoids

NULL (default) or length-k vector of integer indices (in 1:n) specifying initial medoids instead of using the ‘build’ algorithm.

stand

logical; if true, the measurements in x are standardized before calculating the dissimilarities. Measurements are standardized for each variable (column), by subtracting the variable's mean value and dividing by the variable's mean absolute deviation. If x is already a dissimilarity matrix, then this argument will be ignored.

cluster.only

logical; if true, only the clustering will be computed and returned, see details.

do.swap

logical indicating if the swap phase should happen. The default, TRUE, correspond to the original algorithm. On the other hand, the swap phase is much more computer intensive than the build one for large $n$, so can be skipped by do.swap = FALSE.

keep.diss, keep.data

logicals indicating if the dissimilarities and/or input data x should be kept in the result. Setting these to FALSE can give much smaller results and hence even save memory allocation time.

pamonce

logical or integer in 0:5 specifying algorithmic short cuts as proposed by Reynolds et al. (2006), and Schubert and Rousseeuw (2019) see below.

trace.lev

integer specifying a trace level for printing diagnostics during the build and swap phase of the algorithm. Default 0 does not print anything; higher values print increasingly more.

##### Details

The basic pam algorithm is fully described in chapter 2 of Kaufman and Rousseeuw(1990). Compared to the k-means approach in kmeans, the function pam has the following features: (a) it also accepts a dissimilarity matrix; (b) it is more robust because it minimizes a sum of dissimilarities instead of a sum of squared euclidean distances; (c) it provides a novel graphical display, the silhouette plot (see plot.partition) (d) it allows to select the number of clusters using mean(silhouette(pr)[, "sil_width"]) on the result pr <- pam(..), or directly its component pr$silinfo$avg.width, see also pam.object.

##### References

Reynolds, A., Richards, G., de la Iglesia, B. and Rayward-Smith, V. (1992) Clustering rules: A comparison of partitioning and hierarchical clustering algorithms; Journal of Mathematical Modelling and Algorithms 5, 475--504. 10.1007/s10852-005-9022-1.

Erich Schubert and Peter J. Rousseeuw (2019) Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms; Preprint, (https://arxiv.org/abs/1810.05691).

agnes for background and references; pam.object, clara, daisy, partition.object, plot.partition, dist.

• pam
##### Examples
# NOT RUN {
## generate 25 objects, divided into 2 clusters.
x <- rbind(cbind(rnorm(10,0,0.5), rnorm(10,0,0.5)),
cbind(rnorm(15,5,0.5), rnorm(15,5,0.5)))
pamx <- pam(x, 2)
pamx # Medoids: '7' and '25' ...
summary(pamx)
plot(pamx)
## use obs. 1 & 16 as starting medoids -- same result (typically)
(p2m <- pam(x, 2, medoids = c(1,16)))
## no _build_ *and* no _swap_ phase: just cluster all obs. around (1, 16):
p2.s <- pam(x, 2, medoids = c(1,16), do.swap = FALSE)
p2.s

p3m <- pam(x, 3, trace = 2)
## rather stupid initial medoids:
(p3m. <- pam(x, 3, medoids = 3:1, trace = 1))

# }
# NOT RUN {
pam(daisy(x, metric = "manhattan"), 2, diss = TRUE)

data(ruspini)
## Plot similar to Figure 4 in Stryuf et al (1996)
# }
# NOT RUN {